REVIEWS 161 



by the new Chapters 3 and 4 on Continuous Functions and Uniform Convergents, 

 and on the Theory of Riemann Integration. The old Chapters 3, 5, 6, 7 and 8 

 still stand with changed numbers. But three more new chapters have been 

 added to the First Part, namely on Fourier's Series, Linear Differential Equations, 

 and Integral Equations. 



In the Second Part all the eight chapters of the first edition still stand, but the 

 single chapter on Hypergeometric Functions is now replaced by two, while the 

 three original chapters on Elliptic Functions are now put into one chapter or are 

 otherwise distributed. The new chapters in the second edition are named, The 

 Zeta-Function of Riemann, The Confluent Hypergeometric Function, The Mathiew 

 Functions, The Theta Functions, and the Jacobean Elliptic Functions. 



We rather miss the detailed table of contents in the first edition, which is now 

 replaced by a single list of contents including only chapters. On the other hand, 

 to make up for this, the new edition contains an excellent list of authors quoted 

 and also a general index in place of the original rather scanty index of terms 

 employed. It will thus be apparent that the changes are considerable. The 

 work is so well done that one can usually find in it most of the matter now being 

 often brought out separately in the form of small mathematical volumes, and is 

 therefore indispensable, both for workers and teachers. The new edition contains 

 a total of 560 pages against a total of 378 pages in the first edition. 



A Treatise on Electricity. By F. B. Pidduck, Fellow of Queen's College, 

 Oxford. [Pp. xiv + 646, with 369 illustrations.] (Cambridge : at the 

 University Press, 1916. Price 14s. net.) 



The enormous development of the modern branches of electricity in the last 

 decade has produced a large number of monographs and special treatises which 

 have been written by specialists for the benefit of the advanced worker. These 

 books are very formidable, not to say bewildering, to the student, faced as he is 

 with the necessity of knowing something of each subject for his final examination 

 and lacking the time and the experience necessary to enable him to pick out for 

 himself their more important parts. Much of the matter they contain is still in a 

 state of flux, but there is a great deal whose position and relative importance in 

 the main structure have become quite definite, and a complete treatise incorporat- 

 ing such fundamental facts is considerably overdue. Mr. Pidduck has undertaken 

 the task and his book will become henceforth an almost indispensable part of a 

 third year's reading for Physics Honours. To cover so much ground in a single 

 volume makes the problem of selection a very difficult one, and in this matter the 

 author has achieved a notable success. Magnetism has perhaps been rather 

 neglected — there is, for example, no reference to Langevin's theory and its later 

 developments — but the conflicting claims^of the theoretical and experimental sides 

 of the subject have been balanced most admirably. There is even a chapter of 

 sixty pages devoted to applied electricity which contains just the knowledge that 

 ought to be in possession of the student of pure Physics, whose course too 

 frequently omits all reference to such mundane things as dynamo characteristics 

 and A.C. motors. 



No attempt has been made to avoid the mathematics which is essential to the 

 full comprehension of the subject, but for the most part it is put very clearly. In 

 the discussion of the screening effect of a hollow iron sphere, as in one or two 

 other cases, the author assumes the particular form of the potential functions which 

 satisfy the equations of condition. This of course shortens the work considerably, 

 II 



